login
Slowest growing sequence of semiprimes having the semiprime-pairwise-sum property: for any i<j, a(i)+a(j) is semiprime.
4

%I #14 Jun 14 2018 01:41:08

%S 4,6,51,115,511,5263,116623,204091,823363,1144363,78325123,883337023,

%T 6860264683,19613836423,167589841663

%N Slowest growing sequence of semiprimes having the semiprime-pairwise-sum property: for any i<j, a(i)+a(j) is semiprime.

%e Resulting semiprimes are:

%e {10,55,119,515,5267,116627},

%e {57,121,517,5269,116629},

%e {166,562,5314,116674},

%e {626,5378,116738},

%e {5774,117134},

%e {121886}.

%t spQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; L = {0, 4}; Do[n = L[[-1]] + 1; While[! AllTrue[n + L, spQ], n++]; AppendTo[L, n], {9}]; Rest@ L (* _Giovanni Resta_, Jun 13 2018 *)

%Y Cf. A001358, A164979, A181620.

%K more,nonn

%O 1,1

%A _Zak Seidov_, Feb 21 2006

%E Three more terms from _R. J. Mathar_, Jan 23 2008

%E a(11)-a(12) from _Donovan Johnson_, Nov 11 2008

%E a(13) from _Donovan Johnson_, Jul 22 2011

%E a(14) from _Giovanni Resta_, Jun 13 2018

%E a(15) from _Giovanni Resta_, Jun 14 2018